Mathematical Biology Seminar: Chad Topaz

Abstract

 

Locusts exhibit two interconvertible phases, solitarious and gregarious. Solitarious (gregarious) individuals are repelled from (attracted to) others, and crowding biases conversion towards the gregarious form. We construct a nonlinear partial integrodifferential equation model of the interplay between phase change and spatial dynamics leading to the formation of locust hopper bands. Analysis of our model reveals conditions for the onset of aggregation, characterized by a large scale transition to the gregarious phase. A model reduction to ordinary differential equations describing the bulk dynamics of the two phases enables quantification of the proportion of the population that will gregarize, and of the time scale for this to occur. Numerical simulations provide descriptions of the swarm structure and reveal transiently traveling clumps of gregarious insects. This is joint work with Maria D'Orsogna, Leah Edelstein-Keshet, and Andrew Bernoff.